时间序列新息异常值稳健诊断新方法

A New Robust Diagnosis Method for Innovation Outliers in Time Series

文章分析了已有研究提出的时间序列新息异常值诊断法的不稳健性,并从以下两点对其进行稳健改进:一是构建稳健ARMA模型,确保基于该模型得到的残差不受异常值干扰;二是采用无偏Shamos估计量作为残差标准差σ的稳健估计量。通过以上改进,得到了新息异常值稳健诊断统计量。在模拟样本量分别为50、100、200、500,污染率分别为1%、5%、10%时比较传统诊断法与稳健诊断法的诊断效果,结果发现:传统诊断法受异常值干扰较大,在每种样本量下,随着污染率增加,诊断正确率急速下降,特别是在高污染率(10%)下,已基本无诊断力,而稳健诊断法不受异常值干扰,正确率均为100%。随后将稳健诊断法应用于金融时间序列异常值诊断,诊断结果与实际情况相吻合。

This paper analyzes the non-robustness of the time series innovation outlier(IO) diagnosis method proposed byprevious researches, and makes a robust improvement on it from the following two points: First, construct a robust ARMA model to ensure that the residual based on the model is not disturbed by outliers;second, the unbiased Shamos estimator is used as the robust estimator for residual standard deviation σ. Through the improvement above, the robust diagnosis statistics of innovation outliers are obtained. After comparing the effect of traditional diagnosis with that of robust diagnosis when the simulated sample size is 50, 100, 200 and 500 and the pollution rate is 1%, 5% and 10%, respectively, the paper comes to the following findings:The traditional diagnosis method is greatly disturbed by outliers;under each sample size, the diagnostic accuracy decreases rapidly with the increase of pollution rate;especially for high pollution rate(10%), there is almost no diagnostic capacity, but the robust diagnosis method is not disturbed by outliers, and the accuracy is 100%. Finally, the paper applies the robust diagnosis method to the outlier diagnosis of financial time series, and the diagnosis results are consistent with the actual situation.